In the case of interference originating from a given direction, a solution consists in disposing an array of sensors and in weighting the various channels of the sensors so as to partially or totally reject the disturbing signal originating from this direction. This therefore involves a spatial weighting.
Various adaptive algorithms currently exist for calculating the weights to be allocated to the various channels in order to decrease the impact of interference; rejection is generally performed.
Iterative algorithms are known, such as the Appelbaum algorithm, the stochastic gradient algorithm, the least squares algorithm, . . . , based on minimizing the mean square error or on maximizing the signal-to-noise ratio.
Another solution consists in applying the power inversion algorithm also called the Capon algorithm based on minimizing the power at the output of the array of sensors. This algorithm may also be used in instantaneous mode (also known as “snapshot” mode) or in an iterative implementation. The main steps of the Capon algorithm in instantaneous mode will be described.
Represented diagrammatically in FIG. 1 is an array of sensors Ci receiving a disturbing signal modeled by an incident plane wave of wavelength λ.
At the output of the array of K sensors, the signal Sout is of the form:
                    S        out            ⁡              (        t        )              =                            W          app1                ⁢                  S          1                    +                        W          app2                ⁢                  S          2                    +      …        ⁢          ,            i      .      e      .                          ⁢                        S          out                ⁡                  (          t          )                      =                  ∑                  i          =          1                K            ⁢              (                              W                          app              i                                ·                                    S              i                        ⁡                          (              t              )                                      )            Wappi being the gain (or weighting) Wi applied to sensor Ci and Si being the time signal originating from sensor Ci.
The output power P of the type E[|Sout·S*out|], E being the expectation integrated over a long time (tending to infinity), is expressed in the form:P=WappH·RSS·Wapp,with Wapp=(Wapp1, Wapp2 . . . WappK), WappH representing the hermitian (that is to say the conjugate transpose) of the weighting vector Wapp, and RSS being the correlation matrix for the signals Si of the various sensors.
      R    SS    =      [                                        r            11                                                r            21                                    ⋯                                      r            K1                                                            r            12                                                r            22                                    ⋯                                                                                      ⋯                          ⋯                                                                                                                                                  r                          1              ⁢              K                                                ⋯                                                                                      r            KK                                ]  with rik(t)=Si(t)·SkH(t).
A trivial solution making it possible to minimize the power P is: Wapp=0. To avoid this trivial solution, a constraint C is imposed on the weighting coefficients. For example, a possible constraint is such that:
Wapp.C=1.
The solution under the constraint C is given by:
      W    cal    =                    R        SS                  -          1                    ⁢      C                      C        H            ⁢              R        SS                  -          1                    ⁢      C      and we have: Wapp=Wcal*.
The rejections obtained by the various algorithms are illustrated in FIG. 2: the iterative algorithms result in a lowering of the level of the interference “Int” virtually to the level of the thermal noise (case a of FIG. 2) and the Capon algorithm lowers the level of the interference under the level of the thermal noise to a value symmetric with the starting value (case b of FIG. 2). The limit of sensitivity of these algorithms is fixed with respect to the thermal noise.
These algorithms then exhibit difficulties of rejection for interference whose power is low, but already sufficient to degrade the performance of the receivers.